Question

1.You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p = 0.6. You would like to be 98% confident that your estimate is within 1.5% of the true population proportion. How large of a sample size is required?

2. You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 65%. You would like to be 95% confident that your estimate is within 2% of the true population proportion. How large of a sample size is required? Do not round mid-calculation.

Answer 1

Solution :

Given that,

= 0.6

1 - = 1 - 0.6 = 0.4

margin of error = E = 1.5% = 0.015

At 98% confidence level the z is,

= 1 - 98%

= 1 - 0.98 = 0.02

/2 = 0.01

Z_/2 = 2.326 Using z table  

Sample size = n = (Z_/2 / E)² * * (1 - )

= (2.326 / 0.015)² * 0.6 * 0.4

=5771

Sample size = 5771

(b)

Solution :

Given that,

= 0.65

1 - = 1 - 0.65= 0.35

margin of error = E = 2% = 0.02

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96 Using z table  

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.96 / 0.02)² * 0.65* 0.35

= 2185

Sample size = 2185